def test_rotation_matrix_from_angle_known_values(self):
"""
_rotation_matrix_from_angle should give known result with known input.
"""
for angle, matrix in self.known_values:
result = _rotation_matrix_from_angle(angle)
numpy.testing.assert_array_almost_equal(matrix, result)
def test_scaling_transform_matrix_known_values(self):
for rotation, scale, shear, _, _ in SCALING_KNOWN_VALUES:
tform = ScalingTransform(rotation=rotation, scale=scale)
R = _rotation_matrix_from_angle(rotation)
S = scale * numpy.eye(2)
matrix = numpy.dot(R, S)
numpy.testing.assert_array_almost_equal(matrix, tform.transformation_matrix)
def test_roundtrip(self):
"""
_rotation_matrix_to_angle(_rotation_matrix_from_angle(angle)) == angle
for all angles.
"""
for angle in numpy.pi * numpy.linspace(-1, 1, 1000):
matrix = _rotation_matrix_from_angle(angle)
result = _rotation_matrix_to_angle(matrix)
self.assertAlmostEqual(angle, result)
def test_affine_transform_matrix_known_values(self):
for rotation, scale, shear, _, _ in AFFINE_KNOWN_VALUES:
tform = AffineTransform(rotation=rotation, scale=scale,
shear=shear)
R = _rotation_matrix_from_angle(rotation)
S = scale * numpy.eye(2)
L = numpy.array([(1., shear), (0., 1.)])
matrix = numpy.dot(numpy.dot(R, S), L)
numpy.testing.assert_array_almost_equal(matrix, tform.transformation_matrix)
def test_rotation_matrix_properties(self):
"""
Test that the rotation matrix is a 2x2 square orthogonal matrix, with
determinant equal to 1.
"""
for angle in numpy.pi * numpy.linspace(-1., 1., 1000):
matrix = _rotation_matrix_from_angle(angle)
self.assertEqual(matrix.shape, (2, 2))
numpy.testing.assert_array_almost_equal(numpy.dot(matrix.T, matrix), numpy.eye(2))
self.assertAlmostEqual(numpy.linalg.det(matrix), 1.)
def test_similarity_transform_from_pointset_umeyama(self):
"""
SimilarityTransform.from_pointset should return the known results for
the specific known input as described in the paper by Umeyama.
"""
src = numpy.array([(0, 0), (1, 0), (0, 2)])
dst = numpy.array([(0, 0), (-1, 0), (0, 2)])
tform = SimilarityTransform.from_pointset(src, dst)
numpy.testing.assert_array_almost_equal(
_rotation_matrix_from_angle(tform.rotation),
numpy.array([(0.832, 0.555), (-0.555, 0.832)]),
decimal=3,
)
self.assertAlmostEqual(tform.scale, 0.721, places=3)
numpy.testing.assert_array_almost_equal(tform.translation,
numpy.array([-0.800, 0.400]))
self.assertAlmostEqual(tform.fre(src, dst), 0.516, places=3)
def test_similarity_transform_matrix_known_values(self):
for rotation, scale, _, _, _ in SIMILARITY_KNOWN_VALUES:
tform = SimilarityTransform(rotation=rotation, scale=scale)
R = _rotation_matrix_from_angle(rotation)
matrix = scale * R
numpy.testing.assert_array_almost_equal(matrix, tform.transformation_matrix)
def test_rigid_transform_matrix_known_values(self):
for rotation, _, _, _, _ in RIGID_KNOWN_VALUES:
tform = RigidTransform(rotation=rotation)
matrix = _rotation_matrix_from_angle(rotation)
numpy.testing.assert_array_almost_equal(matrix, tform.transformation_matrix)
